Question

Which equation represents a line that passes through (2, -1/2) and has a slope of 3?
O y-2 = 3(x +1/2)
O y-3 = 2(x + 1/2)
O y+ 1/2 = 3(x - 2)
o y + 1/2 = 2(x - 3)

Answer 1

Answer:

$\displaystyle y + \frac{1}{2} = 3\, (x - 2)$.

Step-by-step explanation:

Consider a line in a cartesian plane that goes through the point $(x_{0},\, y_{0})$. If the slope of this line is $m$ (a real constant,) the equation of this line in point-slope form would be:

$y - y_{0} = m\, (x - x_{0})$.

The line in this question goes through the point $(2,\, (-1/2))$. Thus, $x_{0} = 2$ whereas $y = (-1/2)$. The slope of this line is $m = 3$. Thus, the equation of this line in point-slope form would be:

$y - (-1/2) = 3\, (x - 2)$.

Simplify to obtain:

$y + (1/2) = 3\, (x - 2)$.